In physics, wave-particle duality holds that light and matter simultaneously exhibit properties of waves and of particles. This concept is a consequence of quantum mechanics.

In 1905, Einstein reconciled Huygens' view with that of Newton. He explained the photoelectric effect (an effect in which light did not seem to act as a wave) by postulating the existence of photons, quanta of energy with particulate qualities. Einstein postulated that the frequency of light, , is related to the energy, , of its photons:

(2.3)

where is Planck's constant ().

In 1924, De Broglie claimed that all matter has a wave-like nature. He related wavelength and momentum p:

(2.4)

This is a generalization of Einstein's equation above, since the momentum of a photon is given by

(2.5)

where is the speed of light in vacuum, and .

De Broglie's formula was confirmed three years later by guiding a beam of electrons (which have rest mass) through a crystalline grid and observing the predicted interference patterns. Similar experiments have since been conducted with neutrons and protons. Authors of similar recent experiments with atoms and molecules claim that these larger particles also act like waves. This is still a controversial subject because these experimenters have assumed arguments of wave-particle duality and have assumed the validity of de Broglie's equation in their argument.

The Planck constant h is extremely small and that explains why we don't perceive a wave-like quality of everyday objects: their wavelengths are exceedingly small. The fact that matter can have very short wavelengths is exploited in electron microscopy.

In quantum mechanics, the wave-particle duality is explained as follows: every system and particle is described by state functions which encode the probability distributions of all measurable variables. The position of the particle is one such variable. Before an observation is made the position of the particle is described in terms of probability waves which can interfere with each other.